Given $ m \angle BOC = 3x + 20$, $ m \angle AOB = 3x + 100$, and $ m \angle AOC = 150$, find $m\angle BOC$. $O$ $A$ $C$ $B$
From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {3x + 100} + {3x + 20} = {150}$ Combine like terms: $ 6x + 120 = 150$ Subtract $120$ from both sides: $ 6x = 30$ Divide both sides by $6$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 3({5}) + 20$ Simplify: $ {m\angle BOC = 15 + 20}$ So ${m\angle BOC = 35}$.